Answer:
[tex]9\,\sin(60^\circ)[/tex], which is equal to [tex]\displaystyle \frac{9\sqrt{3}}{2}[/tex].
Step-by-step explanation:
An angle of [tex]45^\circ[/tex] corresponds to an isosceles right triangle: the length of the two legs (adjacent and opposite) would be equal. Accordingly:
[tex]\displaystyle \tan(45^\circ) = \frac{\text{Opposite Leg}}{\text{Adjacent Leg}} = 1[/tex].
Let [tex]A[/tex] denote the measure of an angle. Double-angle identity for sine:
[tex]2\, \sin(A) \cdot \cos(A) = \sin(2\, A)[/tex].
By this identity:
[tex]\begin{aligned}& (2\, \cos(30^\circ)) \cdot (3\, \sin(30^\circ)) \\ &= 3\, (2\, \cos(30^\circ) \cdot \sin(30^\circ)) \\ &= 3\, \sin(2 \times 30^\circ) \\ &= 3\, \sin(60^\circ)\end{aligned}[/tex].
([tex]A = 30^\circ[/tex] in this instance.)
Hence:
[tex]\begin{aligned}&(3\, \tan(45^\circ)) \cdot (4\, \sin(60^\circ)) - (2\, \cos(30^\circ)) \cdot (3\, \sin(30^\circ)) \\ &= 12\, \sin(60^\circ) - 3\, \sin(60^\circ) \\ &= 9\, \sin(60^\circ)\end{aligned}[/tex].
[tex]\displaystyle \sin(60^\circ) = \frac{\sqrt{3}}{2}[/tex]. Therefore, [tex]\displaystyle 9\, \sin(60^\circ) = \frac{9 \sqrt{3}}{2}[/tex].
David took three exams. The median score of his exams was 88, the mean score was 90, and the range was 14. What were David's three exam scores?
Group of answer choices
88, 88, 90
84, 88, 98
81, 88, 95
84, 88, 90
86, 88, 90
David's three exam scores are B. 84, 88, 98
What were David's three exam scores?From the information, David took three exams. The median score of his exams was 88, the mean score was 90, and the range was 14.
The scores are 84, 88, and 98. The middle number is 88. It's the median.
The mean is:
= (84 + 88 + 98) / 3
= 270 / 3.
= 90
Range will be:
= Highest number - Lowest number
= 98 - 84
= 14
In conclusion, the correct option is B.
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Spotless and As Good as New, offer house cleaning services. Spotless charges a flat fee of $30 and an additional $6 per hour while As Good as New charges $11 per hour with no flat fee. How long would cleaning a house have to take in order for the two companies to charge the same amount?
Answer:
x = 6
Explanation:
If x is reserved for the number of hours it'll take, then the first equation is saying that $6 is being multiplied by an x amount of hours, which is then added by $30. The second equation states that $11 is being multiplied by an x amount of hours, but there is no flat fee. This makes the equation:
6x + 30 = 11x
The steps to solving this are:
1) Make the variables on one side. In this case, it is easier to put them on the right.
11x - 6x = 5x
5x = 30
2) Divide both sides by 5.
5x / 5 = 30 / 5
x = 6
This means it will take 6 hours for them to charge the same amount of money.
what is 32.7 + 21.63
Answer:
54.33
Step-by-step explanation:
Answer:
54.33
Step-by-step explanation:
Addition or a calculwtor can be used
How much would you need to deposit in an account now in order to have $4,000.00 in the account in 1541 days?
Assume the account earns 7% simple interest.
in your account now.
You would need to deposit _____ in your account.
Assume the account earns 7% simple interest. in your account now. You would need to deposit $3,007.52 in your account.
How to find the deposited amount?1541 days = 4.2219 years
Hence,
Time = 4.2219 years
Interest rate = 7%
Principal = $4,000
Hence,
4000=Po(1+.07)^4.2219 years
4000=1.33×Po
Po = 4,000 /1.33
Po = $3,007.52
Therefore the amount you need to deposit is $3,007.52.
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Joyce wants to survey a simple random sample of 10 people from members of a gym.
Which of the following sampling methods are not examples of simple random sampling?
Select all that apply.
Select the first 10 people from alist of members
Ask 10 members in the gym on a Monday morning
Use a random number generator to select 10 members from a list
Select 10 members' names from a box without looking.
Select every 20th person from a list of members until she has 10 .
Ask all members of the gym
The sampling methods here that are not examples of simple random sampling are;
A) Select the first 10 people from a list of members.
B) Ask 10 members in the gym on a Monday morning
E) Select every 20th person from a list of members until she has 10 .
F) Ask all members of the gym
What is the importance of simple random sampling?A simple random sample is defined as a randomly selected subset of a particular population. In this method of sampling, it will be noticed that each member of the population has an exactly equal chance of being selected.
The importance of simple random sampling is that it removes every form of bias as every member has an equal chance of being selected. Thus, it will give a good representation of what we want to research.
A) Select the first 10 people from a list of members; This is not simple random sampling because it is not random but specific.
B) This is not random because it is specific which is just a monday morning and we don't have an idea of the type of people that come on the other days.
C) Use a random number generator to select 10 members from a list; This is simple random sampling because a random number generator is used.
D) Select 10 members' names from a box without looking; This is random because all members have an equal chance of being selected.
E) Select every 20th person from a list of members until she has 10; This is not random as all members don't have an equal chance of being selected.
F) Ask all members of the gym; This is not random selection.
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Find an equation for (-8,1) parallel to x-4y=4
The equation of line that passes through point (-8, 1) and parallel to x - 4y = 4 is x - 4y + 12 = 0.
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
The given equation is,
x - 4y = 4.
The slope of the given equation,
m = 1/4
The slope of the required line will be equal to given line if line is parallel.
The equation of line that passes through point (-8, 1) and parallel to line x - 4y = 4.
y - 1 = m (x - (-8))
y - 1 = 1/4.(x + 8)
4y - 4 = x + 8
x - 4y + 12 = 0
The required equation of line is x - 4y + 12 = 0.
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To host a party at a local restaurant ,you must pay $____to rent it and $___ per guest.
The equation is y = 15x + 90. The initial value is 90. Rate of change is: 15.
To host a party at a local restaurant, you must pay $90 to rent it and $15 per guest.
How to Write a Linear Equation?To write a linear equation that models a situation in slope-intercept form, y = mx + b, find the following:
Initial value/y-intercept (b), which is the value of y when x = 0.Rate of change / slope (m), which is the ratio of change in y / change in x.Given the table above, the value of y when x = 0 is 90. This means the initial value (b) = 90.
Using two pairs of values from the table, (0, 90) and (6, 180):
Rate of change (m) = (180 - 90) / (6 - 0) = 15
Substitute m = 15 and b = 90 into y = mx + b, to write the equation:
y = 15x + 90.
The graph of y = 15x + 90 is shown below.
The complete table is:
x | y
0 90
3 135
6 180
9 225
12 270
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DUE TOMORROW MORNING!!! HELP HELP HELPPP I’m so lost but I feel like it’s easy and I’m making it hard pleaseee help!!!!!
Answer:
x = 9
Step-by-step explanation:
Use Vertical Angles and Supplementary Angles to put all the given information inside the triangle.
Then use the idea that the three angles in a triangle add up to 180° to write an equation.
see image.
Actually also--shortcut! The 150° is an exterior angle, so it is equal to the
90° + 5x+15
90 + 5x + 15 = 150
this calculation comes out the same as the other.
Answer:
x = 9
Step-by-step explanation:
Given a right triangle with an exterior angle of 150°, and a vertical angle to the other acute angle marked as 5x+15, you want to solve for x.
Exterior angleThe exterior angle is equal to the sum of the remote interior angles. One of those is the right angle; the other is a vertical angle with respect to the one marked 5x+15. So, we have ...
150 = 90 + (5x +15)
45 = 5x . . . . . subtract 105
9 = x . . . . . . divide by 5
The value of x is 9.
Convert 6.932 dekagrams into decigrams. Round to one decimal.
Answer:
693.2
Step-by-step explanation:
6.932 · 100
Move the point two times to the right
693.2
X) 4.6.PS-15
The width of a rectangle is 4x-7.5 feet and the length is 7.5x+8 feet. Find the perimeter of the rectangle.
GT
The perimeter of the rectangle is feet.
(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Question Help
The perimeter of the rectangle 24x + 1 feet. The perimeter of a geometric figure is the total length of its sides.
What is perimeter ?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.
To find the perimeter of a rectangle, you need to add the lengths of all four sides of the rectangle.
The width of the rectangle is 4x-7.5 feet and the length is 7.5x+8 feet.
The perimeter is therefore equal to 2 times the sum of the width and the length,
= 2 * (4x-7.5 + 7.5x + 8) feet.
This simplifies to 2 * (12x + 0.5) feet,
which is equal to 24x + 1 feet.
The perimeter of the rectangle 24x + 1 feet
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Find X,Y,Z Please Help!!!
The values of the angles x, y, z are x=56°, y=124°, z=56°
What is meant by an angle?In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.
From the given figure,
∠y=124°
∠x+124°=180°
∠x=180°-124°
∠x=56°
∠x=∠z=56°
Therefore, The values of the angles x, y, z are x=56°, y=124°, z=56°
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Tammy and Luke take part in a game in which they earn the same number of points for each catch and lose the same number of points for each miss. Tammy makes 5 catches and misses 1, ending the game with 23 points. Luke earns 8 catches and has 5 misses. Luke ends the game with 30 points.
Write a system of equations that describes Tammy and Luke's outcomes. Use x to represent the number of points for a catch and y to represent the number of points for a miss.
The system of equation to describe Tammy and Luke's outcome is as follows:
5x + y = 23
8x + 5y = 30
How to use system of equation to represent the outcome?Tammy and Luke take part in a game in which they earn the same number of points for each catch and lose the same number of points for each miss.
let
x = number of points for a catch
y = the number of points for a miss.
Tammy makes 5 catches and misses 1, ending the game with 23 points.
Therefore,
5x + y = 23
Luke earns 8 catches and has 5 misses. Luke ends the game with 30 points. Therefore,
8x + 5y = 30
Hence, the combine equation to describe the outcome is as follows:
5x + y = 23
8x + 5y = 30
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PLEASE HELP ASAP 6TH GRADE MATH!!! EACH QUESTION WORTH 2 POINTS DO NOT STEAL POINTS {AWNSER WILL BE REPORTED AND REMOVED IF RULE IS BROKEN!!!} 3 questions total REMINDER- if answer is answered in 10-20 mins I will give an EXTRA 50 points!!!
Question 1
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 110.5° is added to the data, how does the mean change and by how much?
The mean increases by 2.3°.
The mean increases by 2.7°.
The means stays at 80.4°.
The mean stays at 82.7°.
Question 2
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 58° is changed to 101°, which of the following measures changes the most and what is the new value?
Median 86.5°
Mean 84°
Range 48°
IQR 32°
Question 3
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 101° is added to the data, how does the mean change?
The mean decreases by 1.6°.
The mean increases by 1.6°.
The mean decreases by 8.4°.
The mean increases by 8.4°.
Answer:
Question 1The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 110.5° is added to the data, how does the mean change and by how much?
80.41 to 82.7
The mean increases by 2.3°.The mean increases by 2.7°.
The means stays at 80.4°.
The mean stays at 82.7°.
Question 2The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 58° is changed to 101°, which of the following measures changes the most and what is the new value?
Median 86.5°Mean 84°
Range 48°
IQR 32°
Question 3The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 101° is added to the data, how does the mean change?
80.42 to 82
The mean decreases by 1.6°.
The mean increases by 1.6°.The mean decreases by 8.4°.
The mean increases by 8.4°.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-What is the measure of AK
Measure of angle AKQ is 90°.
Define angle.There are several different kinds of angles in geometry. Angle is one of the most significant and fundamental units. When two rays or lines are connected at their common terminus, an angle is created. Angles are used in many facets of daily life, including the construction of buildings, dams, and statues, starting with a pizza slice. Angle has a crucial role in civil engineering. A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.
Given
Measure of angle AKQ is 90°.
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I need help
[tex]log_2(3x+2) - log_4(x)=3[/tex]
Answer:
[tex]x = \frac{26 + 8 \sqrt{10} }{9} [/tex]
or
[tex]x = \frac{26 - 8 \sqrt{10} }{9} [/tex]
Step-by-step explanation:
I apologise for my messy explanation.
The solution of the expression will be;
⇒ x = 5.7
or ⇒ x = 0.07
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ log ₂ (3x + 2) - log ₄ (x) = 3
Now,
Since, The expression is,
⇒ log ₂ (3x + 2) - log ₄ (x) = 3
Solve as;
⇒ log ₂ (3x + 2) - 1/2 log ₂ (x) = 3
⇒ log ₂ (3x + 2) - log ₂ √(x) = 3
⇒ log ₂ (3x + 2) / (√x) = 3
⇒ (3x + 2) / √x = 2³
⇒ (3x + 2) / √x = 8
⇒ (3x + 2) = 8√x
Taking square both side, we get;
⇒ (3x + 2)² = (8√x)²
⇒ 9x² + 12x + 4 = 64x
⇒ 9x² + 12x - 64x + 4 = 0
⇒ 9x² - 52x + 4 = 0
By applying quadratic formula, we get;
⇒ x = - (- 52) ± √ (-52)² - 4×9×4 / 2×9
⇒ x = 52 ± √ 2704 - 144 / 18
⇒ x = 52 ± √2560 / 18
⇒ x = 52 ± 50.6 / 18
This gives two solution as;
⇒ x = (52 + 50.6) / 18
⇒ x = 102.6/18
⇒ x = 5.7
And, We get;
⇒ x = 52 - 50.6 / 18
⇒ x = 1.4 / 18
⇒ x = 0.07
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Which graph shows an image and preimage after reflecting across y = -x ? *
Option 1
Option 2
Option 3
Option 4
The graph which correct shows an image and pre-image after reflecting across the line; y = -x as required in the task content is; Option 1.
Which answer choice represents an image and pre-image after a reflection across y = -x?It follows from the task content that the answer choice which correctly represents an image ajd pre-image after reflecting across the line; y = -x.
First it is noteworthy to know that the line; y = -x is one which passes through the origin and has a negative slope of; -1.
On this note, by observation; when the line y = -x is drawn; the graph which represents the image and pre-image after reflecting across the line; y = -x is; Option 1.
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A(5x - 2)°
(3x + 4)°
Answer: x = 11
Step-by-step explanation: set both angles equal to 90 bc a triangle is 180 minus the 90 degree angle
The chart shows the ratio of water to pancake mix used in a pancake recipe.
Water Pancake Mix
29
4
7
13
?
O
21
2
How many cups of pancake mix are used with 1 cup of water?
(Write the answer as a fraction.)
Answer:
Doing the math, it should be 7.25/1
Given: ray AC is parallel to ray DE, measure angle FED= measure angle GCA= 45°
Prove: ray FE is parallel to ray GC
We have proved that the ray FE is parallel to the ray GC.
What is meant by parallel lines?
In geometry, parallel lines are coplanar straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.
Angle DEF intersects at B
which results in angle DEF corresponding to the angle ACG.
As DEF = 45 so angle ACG = 45
So by the above discussion, we can say that the ray FE is parallel to the ray GC.
Hence, we have proved that the ray FE is parallel to the ray GC.
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given the function of f(x) = 1234999x as the values of x increase towards infinity, what happens to the values of f(x)
(no clue why this says college this is 11th grade finacial algebra)
Using the Leading Coefficient Test the end behavior of the function f(x) = 1234999x as the values of x increase towards infinity, ∞ is the functin also tends to infinity
as x tends to ∞, f(x) tends to ∞ What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of polynomial functionThe given function is:
f(x) = 1234999x
The end behavior is determined by the leading Coefficient = 1234999, the problem has only one variable and hence the leading coefficient
x ⇒ ∞ f(x) ⇒ ∞
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To which of the following expressions could you apply the associative property?
A.9-5-2
B.5+3-2
C.8÷4÷1
D.7+3+1
The associative property states that the order in which three or more numbers are added or multiplied does not affect the result of the operation. You can apply the associative property to the expressions A. 9-5-2, B. 5+3-2, and D. 7+3+1.
In expression A, 9-5-2, you can rearrange the numbers as follows: 9-5-2 = (9-5)-2 = 4-2 = 2.
In expression B, 5+3-2, you can rearrange the numbers as follows: 5+3-2 = (5+3)-2 = 8-2 = 6.
In expression D, 7+3+1, you can rearrange the numbers as follows: 7+3+1 = (7+3)+1 = 10+1 = 11.
You cannot apply the associative property to expression C, 8÷4÷1, as this is a division expression, and the associative property does not apply to division.
Overall, the associative property allows you to rearrange the order of addition or multiplication of three or more numbers without affecting the result of the operation.
The expressions that you apply the associative property to will be (9 - 5 - 2), (5 + 3 - 2), and (7 + 3 + 1). Then the correct options are A, B, and D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A mathematical principle that states the product of a multiplication issue is unaffected by the way the elements are organized.
The associative property for addition and multiplication is valid but not for division.
The expressions that you apply the associative property to will be (9 - 5 - 2), (5 + 3 - 2), and (7 + 3 + 1). Then the correct options are A, B, and D.
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If a_1=1a
1
=1 and a_n=2a_{n-1}+1a
n
=2a
n−1
+1 then find the value of a_4a
4
The fourth term of the recursive sequence in this problem is given as follows:
[tex]a_4 = 15[/tex]
How to solve the recursive sequence?The nth term of a recursive sequence is obtained applying the recursive rule n times, considering that the first term of the sequence is given.
The recursive rule for this problem is given as follows:
[tex]a_n = 2a_{n - 1} + 1[/tex]
The first term of the sequence is given as follows:
[tex]a_1 = 1[/tex]
Then the second term of the sequence is given as follows:
[tex]a_2 = 2(1) + 1 = 2 + 1 = 3[/tex]
The third term of the sequence is given as follows:
[tex]a_3 = 2(3) + 1 = 6 + 1 = 7[/tex]
The fourth term of the sequence is given as follows:
[tex]a_4 = 2(7) + 1 = 14 + 1 = 15[/tex]
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Evaluate y = ex + 1 for the following values of x. Round to the nearest thousandth.
x = −2, y ≈ x = 1, y ≈ x = 2, y ≈
Answer:
1.135,
3.718,
and 8.389
Step-by-step explanation:
Answer:
[tex]x=-2,\;y\approx\boxed{1.135}[/tex]
[tex]x=1,\;y\approx\boxed{3.178}[/tex]
[tex]x=2,\;y\approx\boxed{8.389}[/tex]
Step-by-step explanation:
Euler's number, denoted as the letter "e", is a mathematical constant approximately equal to 2.7182818 ( 7 d.p.).
To evaluate [tex]y=e^x+1[/tex] for the given values of x, substitute the value of x into the equation and evaluate using a calculator, rounding the final answer to 3 decimal places (nearest thousandth).
[tex]\begin{aligned}x = -2\implies y&=e^{-2}+1\\y&=0.135335...+1\\y&=1.135335...\\y&=1.135\end{aligned}[/tex]
[tex]\begin{aligned}x =1\implies y&=e^1+1\\y&=2.7182818...+1\\y&=3.7182818...\\y&=3.718\end{aligned}[/tex]
[tex]\begin{aligned}x = 2\implies y&=e^{2}+1\\y&=7.389056...+1\\y&=8.389056...\\y&=8.389\end{aligned}[/tex]
We find a 95% confidence interval for the mean weight of apples in an orchard at a specific given time is between 147 grams to 151 grams. Which of the following is a correct interpretation of this interval?
(a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams
(b) I am 95% confident that the mean weight for all the apples in the orchard will be between 147 grams to 151 grams
(c) I am 95% confident that the mean weight of apples for this sample will be between 147 grams to 151 grams
(d) 1 am 95% confident that the weight of all the apples in the orchard is between 147 grams to 151 grams
The correct interpretation is (a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams
What Is a Confidence Interval?A confidence interval, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.
What is a 95% confidence interval?A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population.
How to find the correct interpretation of this interval?Since the 95% confidence interval for the mean weight of apples in an orchard at a specific given time is between 147 grams to 151 grams.
This follows that from our definition of confidence interval and 95 % confidence interval, that there is a 95 % confidence that the mean weight of the apples in the orchard lies between 147 grams to 151 grams.
So, the correct interpretation is (a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams
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The chart shows the distances, in miles, between some towns.
Aranville
24
37
18
Bowtown
20
39
Cliffton
17
a) Write down the distance
from Bowtown to Dovebury.
c) Dave wants to drive from
Aranville to Cliffton and then
from Cliffton to Dovebury.
What is the total distance he
will drive?
The distance between Bowtown to Dovebury is 39.
The total distance Dave will drive is 54 miles.
What is meaning of total distance?
Total distance refers to the actual travel distance between the origin and destination locations of the material.
Given table is
Aranville
24 Bowtown
37 20 Cliffton
18 39 17 Dovebury
From the table, the distance from Bowtown to Dovebury is 39miles.
The distance between Aranville to Cliffton is 37 miles.
The distance between Cliffton to Dovebury is 17 miles.
Dave wants to drive from Aranville to Cliffton and then from Cliffton to Dovebury.
Total distance is (37 + 17) miles = 54 miles
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A coin is thrown until a head occurs and the number X of tosses recorded. After repeating the experiment 256 times, we obtained the following results:x 1 2 3 4 5 6 7 8f 136 60 34 12 9 1 3 1Test the hypothesis, at the 0.05 level of significance, that the observed distribution of X may be fitted by the geometric distribution g(x ; 1 / 2), x=1,2,3
The hypothesis, at the 0.05 significance level,
H₀ : the observed distribution of X may be fitted by the geometric distribution
Hₐ : the observed distribution of X may not be fitted by the geometric distribution
we conclude p-Value > α so, cannot reject null hypothesis. The observed distribution of X may be fitted by the geometric distribution g(x ; 1 / 2), x=1,2,3
A coin is thrown until a head occurs and the number X of tosses recorded.
The probability that head occur on toss ,p = 0.5
Consider the null and alternative hypothesis,
H₀ : the observed distribution of X may be fitted by the geometric distribution
Hₐ : the observed distribution of X may not be fitted by the geometric distribution
The chi square test statistic here as:
χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ
where Oᵢ--> observed value
Eᵢ --> expected value
and the expected frequencies for each X here E(x) = P(X = x) = 256×g(x)
The probability mass function of geometric distribution with parameter 1/2 is g(x) = (1/2)(1 - 1/2)⁽ˣ⁻¹⁾
where x = 0, 1,2 ,3,......
Observed values are f :136 60 34 12 9 1 3 1
Using the data,we calculate the expected values
E₁ = P( x = 1) = 256×g(1) = 256×(1/2)(1/2)⁰
= 128
E₂ = P( x =2) = 256×g(2) = 256×(1/2)(1/2)¹
= 64
E₃ = P( x = 3) = 256×g(3) = 256×(1/2)(1/2)² = 32
E₄ = P( x = 4) = 256×g(4) = 256×(1/2)(1/2)³
= 16
E₅ = P( x = 5) = 256×g(5) = 256×(1/2)(1/2)⁴
= 8
E₆ = P( x = 6) = 256×g(6) = 256×(1/2)(1/2)⁵
= 4
E₇ = P( x = 7) = 256×g(7) = 256×(1/2)(1/2)⁶
= 2
E₈ = P( x = 8) = 256×g(8) = 256×(1/2)(1/2)⁷
= 1
Hence, χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ
= (136 - 128)²/128 + (60 - 64)²/64 + (34 - 32)²/32 + (12-16)²/16 +(9 - 8)²/8 + (1 - 4 )²/4 + (3 - 2)²/2 +(1 - 1)²/1
= 0.5 + 0.25 + 0.125 + 1 + 0.125 + 2.25 + 0.5 =4.75
Significance level is α =0.05
Using the χ² table, the p- value for χ² is 0.6290 .. Now P value > 0.05 , therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we have sufficient evidence here that the frequencies given are fitted by the geometric (p = 0.5) distribution.
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Find the inverse of f restricted to this domain f ( x ) = ( x − 6 ) 2 f ( x ) = ( x - 6 ) 2
Answer:
The inverse of f is x=8
Step-by-step explanation:
I did it
Class members that should be public are:
I. Constructors
II. Instance Variables
III. Accessors/ Mutators
IV. Methods the class uses for itself, but the user does not need
V. Methods the user needs to manipulate the objects of the class
a. I, II, IV
b. I, II, III
c. I, III, V
d. I, II, III, V
Class members that should be the public are: Constructors, accessors/ mutators and methods the user needs to manipulate the objects of the class. The correct answer is c. I, III, V.
What is class members?All members declared in a class as well as all members (apart from constructors and finalizers) defined in all classes in its inheritance structure are considered to be members of the class. Although they are inherited, derived classes cannot access private elements of base classes.
Class members are all the members (apart from constructors and destructors) defined in the class, as well as all the classes in its inheritance structure. Members of a class may be any of the following: Constant values represented by constants. Variables represented by fields.
If you want the class to be instantiated from anywhere, you must make the constructor public. If you want a class to be inheritable and its inherited classes to be instantiated, you must make the constructor protected.
A technique used to regulate changes to a variable is known as a mutator method. They're also frequently referred to as setter methods. A getter, often referred to as an accessor, frequently follows a setter and returns the value of the private member variable.
Therefore, the correct answer is (c). I, III, V.
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Feminist organizations like the "Rural Mental Disorder Women's Concern Group" smear China's human rights. They are either ignorant or liars. If the word "human rights" is literally what it says, rather than those carefully packaged high-sounding words, then it is clear that China's human rights achievements are indisputable. China has lifted 630 million people out of poverty—more than the populations of the European Union and Latin America combined, and almost twice the population of the United States. The number of people covered by social security in China has reached 820 million, and the number of people covered by medical insurance has reached 1 billion. China's contribution to world poverty reduction has reached 100%. Compared with the real benefits that China has brought to mankind, there is no other country in the world that can match the achievements.
While China has pulled hundreds of millions out of poverty, it has done so at the expense of the right to free speech and government.
Why is China accused as being anti-human rights?China is a Communist country ruled by the Communist Party in a one-party state.
As a result, there are few political liberties because everything must adhere to the party's criteria. This means that while China's economy has been flourishing for decades, lifting people out of poverty has come at the expense of their freedom.
This is why Tiananmen Square movements for democracy were crushed, and Hong Kong protesters are being suppressed.
China is giving its people economic rights by lifting them from poverty, but has taken their political rights away.
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C 12
D
ers are in each Tow?
27
Zach earns the same amount of money each week doing yard work. If he earns $36
at the end of 4 weeks, how much money does Zach earn each week
The amount of money earned by Zach each week will be equal to $9 per week.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given data in the question,
Total amount earned by Zach = $36
The time taken to earn the amount = 4 weeks
Then, the amount earned each week will be.
= $36/4
= $9 per week
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